Find the missing x - and y-values and Pythagorean triples can be generated using the identity given. Write the triple in parentheses, without spaces between the values, with a comma between values, and in order from least to greatest.

The complete question is:

Find the missing x - and y-values and Pythagorean triples using the identity given:

(x² - y²) ² + (2xy) ² = (x² + y²) ²

X Value: 4

Y Value: 3

Pythagorean Triples:?

X Value: 5

Y Value:?

Pythagorean Triples: (9,40,41)

X Value:?

Y Value: 3

Pythagorean Triples: (27,36,45)

X Value: 7

Y Value: 5

Pythagorean Triples:?

Step-by-step explanation:

Pythagorean triples are three numbers p, q, r, that satisfy Pythagoras' theorem.

That is, they are numbers such that

r² = p² + q².

Given the identity

(x² - y²) ² + (2xy) ² = (x² + y²) ²

We can say tha

p = x² - y²

q = 2xy

r = x² + y²

Now, let us use this to solve the given problems.

X Value: 4

Y Value: 3

p = 4² - 3² = 7

q = 2*3*4 = 24

r = 3² + 4² = 25

Pythagorean Triples: (7,24,25)

X Value: 5

Y Value:? = (4)

q = 2xy = 40

2*5*y = 40

y = 40/10 = 4

Pythagorean Triples: (9,40,41)

X Value:? = (6)

Y Value: 3

2xy = q = 36

2*3*x = 36

x = 36/6 = 6

Pythagorean Triples: (27,36,45)

X Value: 7

Y Value: 5

p = 7² - 5² = 24

q = 2*7*5 = 70

r = 7² + 5² = 74

Pythagorean Triples:? = (24,70,74)